Abstract.
Let {X n ,n≥1} be a strictly stationary sequence of negatively associated random variables with the marginal probability density function f(x), the recursive kernel estimate of f(x) is defined by where h n is a sequence of positive bandwidths tending to 0, as n→∞, K(·) is a univariate kernel function. In this note, we discuss the point asymptotic normality for f n (x).
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Acknowledgement. The authors thank the referee for carefully reading the manuscript and for valuable suggestions which improved the presentation of this paper. This research was partially supported by the National Natural Science Foundation of China (No. 10171079), No.R01-2000-000-00010 and No. 2001-42-D0008 from Korea Research Foundation as well as Wonkwang University Grant in 2003.
Rights and permissions
About this article
Cite this article
Liang, HY., Baek, JI. Asymptotic normality of recursive density estimates under some dependence assumptions. Metrika 60, 155–166 (2004). https://doi.org/10.1007/s001840300302
Issue Date:
DOI: https://doi.org/10.1007/s001840300302